Quaternion quantum neurocomputing

Abstract

Since the introduction of quaternion by Hamilton in 1843, quaternions have been used in a lot of applications. One of the most interesting qualities is that we can use quaternions to carry out rotations and operate on other quaternions; this characteristic of the quaternions inspired us to investigate how the quantum states and quantum operator work in the field of quaternions and how we can use it to construct a quantum neural network. This new type of quantum neural network (QNN) is developed in the quaternion algebra framework that is isomorphic to the rotor algebra [Formula: see text] of the geometric algebra and is based on the so-called qubit neuron model. The quaternion quantum neural network (QQNN) is tested and shows robust performance.

Current survey of Clifford geometric algebra applications

“…Experiments validate performance. Quaternions for rotations and operation on other quaternions inspired an investigation 143 The review of Rau 144 brings together the Lie-algebraic/group-representation perspective of quantum physics and GA, as well as their connections to complex quaternions. Altogether, this may be seen as further development of Felix Klein's Erlangen Program for symmetries and geometries.…”

“…Experiments validate performance. Quaternions for rotations and operation on other quaternions inspired an investigation 143 on how quantum states, quantum operator, and quantum NN (QNN) can work with quaternions. A new type of QNN is developed isomorphic to the rotor subalgebra $$$ C{l}^{+}\left(3,0\right) $$$ of $$$ Cl\left(3,0\right) $$$, based on the qubit neuron model.…”

A Survey on Quaternion Algebra and Geometric Algebra Applications in Engineering and Computer Science 1995–2020

“…Bayro [37] formulates quantum gates for the Lie Group SO(3) using neural networks in the sub-algebra G + 3 . They integrate the fields of neurocomputing, quantum computing, and quantum mechanics in a unifying mathematical framework.…”

Quaternionic Fuzzy Sets

“…As early as in 1843, Hamilton [27] discovered the quaternions as a generalization of complex numbers. Quaternion is an important mathematical tool in physics [28,29], quaternion neural networks [30,31], and computer science [32][33][34].…”